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Optimal sup-norm rates, adaptivity and inference in nonparametric instrumental variables estimation

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  • Xiaohong Chen
  • Timothy M. Christensen

Abstract

This paper makes several contributions to the literature on the important yet difficult problem of estimating functions nonparametrically using instrumental variables. First, we derive the minimax optimal sup-norm convergence rates for nonparametric instrumental variables (NPIV) estimation of the structural function h0 and its derivatives. Second, we show that a computationally simple sieve NPIV estimator can attain the optimal sup-norm rates for h0 and its derivatives when h0 is approximated via a spline or wavelet sieve. Our optimal sup-norm rates surprisingly coincide with the optimal L2-norm rates for severely ill-posed problems, and are only up to a [log(n)]∈ (with ∈

Suggested Citation

  • Xiaohong Chen & Timothy M. Christensen, 2015. "Optimal sup-norm rates, adaptivity and inference in nonparametric instrumental variables estimation," CeMMAP working papers 32/15, Institute for Fiscal Studies.
    • Handle: RePEc:azt:cemmap:32/15
    DOI: 10.1920/wp.cem.2015.3215
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